Please,could you tell me what is correct:"not to do something or to not do something"?.I read this but I didn't get the meaning:Not to or to not

No one here at Language Log Plaza seems to have commented on the cartoon in
The New Yorker of 4/18/05, p. 14, in which one woman says to another, on the street, walking past a restaurant, "I'm moving to France to not get fat."
It's a virtually obligatorily split infinitive. The
not can't move "down" into the VP
get fat, because of the conditions on the VP negator
not. If it moves "up", to before the
to, then we get something with the wrong meaning.
The crucial thing here is that we're dealing with a purpose adverbial
to get fat 'in order to get fat'.
Not in combination with its VP (
get fat) at least implicates agency on the part of the referent of the higher subject; 'in order to not get fat'. (I am not a semanticist, though I play one at Language Log Plaza, so go easy on me here.) But
not to get fat is going to get the wider scope semantically: 'not in order to get fat'. And that's not what this woman wanted to say.
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